Finite element analysis of biaxial cyclic tensile loading of elasto-plastic plate with central elliptical hole

Elements of structures which work in real conditions are quite often affected by variable temperatures and loadings. Nowadays the growth of interest related to the asymptotic behavior of inelastic structures subjected to cyclic loading leads to development of direct and incremental methods of stabilized state determining. If loadings vary and the body deforms elastically, then its durability is defined by fatigue characteristics of materials; destruction comes after a large number of cycles. If the body experiences elasto-plastic deformation, at loadings below the limit, the achievement of a dangerous state at a rather small number of cycles is possible. Thus it is necessary to distinguish two cases. The first case occurs when destruction comes due to the alternation of plastic deformations with different signs (for example, after plastic stretching there is plastic compression, etc.); it is cyclic plasticity (plastic or low-cyclic fatigue). The second case occurs when plastic deformations do notchange signs, but grow with each cycle (the progressing deformation - ratcheting). It leads to the inadmissible accumulation of plastic deformations. Thestudy results present finite-element (FEM) calculations of the asymptotical behavior of an elastoplastic plate with the central elliptic hole under the biaxial cyclic loading for three different materials. Incremental cyclic loading of the sample with the stress concentrator (the elliptic central hole) is performed in the multifunctional finite-element package SIMULIA Abaqus. The ranges of loads found for the shakedown, cyclic plasticity and ratcheting are presented. The obtained results are generalized and analyzed. Convenient normalization is suggested. At the expense of the chosen normalization all computed results corresponding to separate materials stay within one common curve with a minimum scattering of points. The convenience of the generalized chart consists of a possibility to receive the asymptotical behavior of the inelastic structure for those materials which computer calculations were not made.